Some crafty folks over at XDA Developers have coded an FM Radio app for the Droid Bionic. Many folks found it odd that the phone didn't already come with one, and some developers wanted to rectify it. This is the same FM Radio app that wokrs on the Droid 3 and several other Motorola phones. Here's a brief quote of instructions and a download link below:
Note: I find itís easiest to download the file to the device and then click on it from the notification bar to enable the installation. Also, donít forget to allow non-market apps in your settings.
Download: FM Radio .apk for Droid Bionic

Source: BionicForums.net via TalkAndroid and XDA-Developers